ABSTRACT
In this chapter, we approach the end of our guided tour into techniques and methods of large-scale systems, where we focus on decentralized filtering and fault detection based on overlapping decomposition. The material covered is divided into two sections. In the first section, the optimal state estimation in a large-scale linear interconnected dynamical system is considered and a decentralized computational structure is developed. The decentralized filter uses hierarchical structure to perform successive orthogonalization on the measurement subspace of each sub-system in order to provide the optimal estimate. This ensures substantial savings in computation time. In addition, since only low-order subsystem machine equations are manipulated at each stage, numerical inaccuracies are reduced and the filter remains stable for even high-order system. In the second section, the problem of fault detection in linear, stochastic, interconnected dynamic systems is examined. The objective addresses a design approach based on employing a set of decentralized filters at the subsystem level resulting from overlapping decomposition. The malfunctioning sensors can be detected and isolated by comparing the estimated values of a single state from different Kalman filters.
